The interaction between physical dynamics and discrete switching logic in engineering applications, such as automotive safety verification or terrain estimation for planetary rovers [1], can lead to unexpected system behaviors or even catastrophic failures, making overall system analysis and safety verification extremely challenging. Therefore, to ensure safety and meet specific performance requirements, these couplings must be properly incorporated into the system's mathematical representation, requiring the use of both discrete and continuous states, known as a hybrid system model, for which I plan to address secure estimation and learning as follows.

I leverage system properties such as mixed-monotonicity to propose a novel class of bounding functions, i.e, Remainder-Form Decomposition Functions, that can be tractably computed. This enables us to obtain tight reachable sets (tubes) of state trajectories of a very broad class of non-smooth and discontinuous nonlinear systems subject to state constraints, observations and set-valued uncertainties [2], and facilitates designing efficient set-inversion algorithms [2, 3]. This has resulted in several set-valued stable (and optimal) observer designs for different uncertainty set characterizations, such as intervals [4, 5, 6], hyperballs [7], and polytopes [3, 8].

I design algorithms that can effectively propagate uncertainty sets of states and disturbances through nonlinear hybrid dynamics and identify subsets of propagated sets that are compatible with nonlinear system measurements, using tractable methods. Additionally, leveraging theoretical tools such as decomposition functions [2], abstraction techniques [9], and graph-theoretic methods, I aim to deploy the designed reachability analysis and state estimation framework [8, 3, 10] in distributed settings, including multi-agent systems, event-triggered, multi-modal, switched, and hybrid distributed plants. Moreover, I intend to use set-theoretic methods to develop tractable algorithms for computing robust reach-avoid-maintain and invariant sets [11] in hybrid networked systems, which have numerous applications, such as safe optimal control and path planning in autonomous vehicles and robotic systems.

I address the situation where, on top of external uncertainties and distur- bances, our understanding of the system’s model or dynamics is incomplete or imprecise. This can be due to various factors, such as the disparate nature of sensors in a vehicle, errors in the model, unpredictable environments, or adversarial inputs. To handle this challenge, I intend to combine the model-based estimation techniques I have previously developed [13, 14, 15] with set-membership learning methods [9, 12]. The goal is to acquire a guaran- teed approximation of the system dynamics while simultaneously estimating the system states and the adversary’s strategies [1, 16, 17] to make robust and (sub)optimal decisions. This enables designing secure and safe estima- tion, path planning, and control algorithms for complex uncertain CPRS.  

Although cyber-physical coupling introduces new functions and improves the performance of control systems, it also exposes them to new cyber vulnerabilities. When safety-critical systems are compromised or malfunction, they can cause significant harm to operators, users, and the physical components being controlled. For example, accurately estimating the intentions of heterogeneous drivers has become crucially important for safe autonomous driving to avoid catastrophic accidents. Therefore, incidents involving adversaries, such as a malicious driver’s unpredictable actions, have accentuated the need for CPRS security and the development of new designs for resilient estimation, attack mitigation, and control. So, addressing resilient decision-making in uncertain CPRS that are compromised by adversarial agents or unexpected events, such as autonomous intelligent vehicle systems facing drivers with different intentions or smart grids under attacks, is both challenging and valuable. My research aims to tackle this challenge by integrating set-theoretic approaches and robust decision-making frameworks with advanced machine learning techniques as follows.

I design tractable (distributed) algorithms to simultaneously estimate states and unknown inputs/attacks in several classes of nonlinear CPRS [15], assuming that the adversaries and uncertainties impact the system in the worst-case scenario, and no useful a priori knowledge, bound or distribution of the attack signals, nor any statistical characteristics for noise and disturbance signals are available. Further, I am leveraging the knowledge of physical system dynamics as an additional sensor to improve the estimates, which equips me with proper tools to develop attack identification approaches and to efficiently synthesize centralized and distributed control strategies to mitigate the e ects of attacks in such settings [18, 19, 20, 21, 14].

In many switched or hybrid safety-critical CPRS, e.g., networked autonomous vehicle systems and smart grids, modes (such as discrete states, sensor modalities, or types of outliers) can be compromised through switching attacks by adversaries or outliers, in addition to data injection attacks. However, existing outlier detection/mode estimation approaches in such settings rely on restrictive adversarial assumptions. To address this issue, my aim is to develop a multiple-model (MM) framework [18, 19] that includes i) a bank of mode-matched observers that provide input and state estimates for the given mode, ii) a mode estimator that deter- mines the most likely or all compatible modes based on observations, and iii) a global fusion estimator that combines the estimates from the bank of estimators and mode observer. The MM framework offers unified algorithms for resilient state estimation, attack mitigation, and control strategies in the presence of different types of uncertainty models, including stochastic (aleatoric), set-valued (epistemic), combined, distributionally robust uncertainties, as well as random set models.

I am working on designing distributed active estimation, fault detection, and control policies for uncertain networked cyber-physical systems. Specifically, I will explore human-robot coordina- tion/competition scenarios in networked systems, such as autonomous vehicles, and investigate game-theoretic techniques to model the strategic behavior of the agents. Instead of only considering the best worst-case scenario, I plan to incorporate strategic decision-making that takes into account robust control and intention estimation approaches for addressing resiliency in the face of uncertainties. To achieve this, I will develop computationally efficient network communication protocols and apply them in the context of robust dynamic/differential networked games. In this context, agents with different intentions, types, and beliefs will adaptively improve their approximation of other agents’ private objective functions by applying set-membership learning techniques [9, 12]. They will then optimize their own objective functions by making decisions based on different levels of bounded rationality, subject to state dynamics and safety constraints. The ultimate goal is to design a system that can handle uncertain networked CPRS with multiple agents while ensuring safety and resiliency.

Motivated by the need to protect sensitive information in networked CPRS, such as in private ride-sharing or verification problem in autonomous vehicles, or control of privacy-sensitive energy settings, a considerable amount of research has focused on ensuring data privacy. However, existing approaches like differential privacy either sacrifice accuracy or incur high computation or communication overhead. I aim to address this challenge as follows. 

I am investigating alternative designs of privacy-preserving mechanisms, which can make the quantification of privacy and the associated performance loss tractable and reasonable, respectively. Next, utilizing such alternative designs, my objective is to propose tractable and private estimation, verification, control and resource allocation algorithms in networked CPRS. I am leveraging a robust optimization approach to propose a functional perturbation-based privacy-preserving mechanism for non-convex distributed optimization, as well as to characterize the best accuracy that can be achieved by an optimal perturbation [22].

I plan to adapt my previously developed robust set-membership analysis tools [2, 17] to introduce the new notion of guaranteed privacy. As opposed to differential privacy, where, to preserve the privacy of agents or data, the exchanged messages or functions are compromised by stochastic perturbations, in guaranteed privacy-preserving mechanism design [21] the main idea is to perturb the true variables or functions by deterministic but uncertain perturbations in a distributed manner, such that the privacy is preserved, regardless of the utilized optimization, estimation, verification or control algorithm. The introduction of such set-valued perturbations enables the attainment of a quantifiable accuracy via a theoretical upper bound that will be shown to be independent of the chosen algorithms. This will result in designing guaranteed privacy-preserving mechanisms that are optimal in the sense that they minimize the corresponding inaccuracy of the networked CPRS performance due to the perturbations. Furthermore, the designed mechanisms are robust against uncertainties in environment and models, and are resilient against changes in the adversary’s intention and knowledge of the system/setting.

In many complex large-scale CPRS, such as swarm robotics, autonomous vehicles and smart grids, the presence of both malicious agents executing false data injection attacks or unexpected behaviors, together with adversarial eavesdropping agents aiming to extract valuable information, is a legitimate concern. In response to this challenge, I plan to develop model predictive control (MPC) strategies that not only ensure privacy but also demonstrate resilience against false data attacks. The main idea is to deploy set- theoretic methods [2, 5, 14, 18], as well as a guaranteed privacy-preserving mechanism design approach [23], to design resilient and privacy-assured observers that yield secure set-valued state estimates, along with robust predictions of the CPRS trajectory. This will culminate in the synthesis of robust, distributed, resilient, and guaranteed privacy-preserving MPC strategies. Such framework could be extended further to guaranteed-private and resilient strategic decision-making, by deploying robust dynamic games (cf. 2.3).